chapter 3 - Bentham Science

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86 Applications of Spreadsheets in Education The Amazing Power of a Simple Tool Sergei Abramovich conditions introduced in Equation (5.1) it follows that when n=1 one has t1 = 1= C1+C2+ 1 or C1 =−C2; when n=2 one has t2 = 3= C1− 2C1+ 3 whence C1 = 0 and C2 = 0. Thus, tn = n(n+1) , n=1, 2, 3,... (5.4) 2 Similarly, Equations (5.2) and (5.3) can be shown to have the solutions and respectively. 5.3 Triangular Numbers sn = n 2 , n=1, 2, 3,... (5.5) pn = (m−2)n2 +(4−m)n , n=1, 2, 3,... (5.6) 2 5.3.1 Establishing Context for Triangular Numbers In what follows, the use of a spreadsheet will be considered, using Pollak’s [17] terminology, in a “whimsical” context. While it may be argued that problems of whimsy have only superficial connection to the real world [18], the recent use of the term modeling embraces all possible relations between mathematics and the world outside it [19]. It appears that one’s perception of what is whimsical and what is not largely depends on one’s experience; in fact, many of today’s real-life situations seemed like fictions yesterday. Furthermore, the strong relationship that exists between modeling and problem solving suggests the importance for the spreadsheet modeling to be carried out in a whimsical context that very often provides a powerful cognitive milieu for solving problems. For example, Engel [20] explored such “whimsical” contexts as fishing, book reading, and coin tossing. It has been shown that each of these contexts is conducive for using modeling strategies as means of instruction and developing the habit of seeing possible applications of mathematics. Note that context itself does not account for the mathematical content – the latter usually begins with a quantitative inquiry into the former, something that may be referred to as mathematization. We begin with Problematic Situation (PS) 5.1 Once upon a time, Hilton built a hotel in Atlantic City shaped as a long parallelepiped with more than 100 rooms on each storey overlooking the waterline of the ocean. The 13th storey turned out to be a dangerous place to stay: Every night a ghost visited a room there. It was observed (see Fig. (5.1)) that the ghost started with room 1, on the second night he emerged in room 3, on the third night he emerged in room 6, then he emerged in room 10, and so on. After a few such nights the hotel’s manager hired a student from a local college to investigate the behavioral pattern of the ghost by using a spreadsheet. More specifically, the manager wanted to know:
Applications of Spreadsheets in Education The Amazing Power of a Simple Tool, 2011, 107–115 107 Enzyme Kinetics for Novice Learners: Numerical Simulation in Excel Scott A. Sinex ∗ and Barbara A. Gage Department of Physical Sciences and Engineering Prince George’s Community College, Largo, Maryland, USA CHAPTER 6 ∗ Address correspondence to: Prof. Scott A. Sinex, Department of Physical Sciences and Engineering, Prince George’s Community College, Largo, Maryland 20774-2199, USA; Tel: (+1) 301-341-3023; E-mail: ssinex@pgcc.edu Abstract: Through an interactive Excel spreadsheet and accompanying activity, first-year college students explore enzyme kinetics, experimental error, and the behavior of inhibitors. Many “what if” questions drive students to discover how a variety of parameters influence results. Keywords: enzyme kinetics, inhibitors, non-linear regression. 6.1 Introduction Enzyme kinetics [1, 2] finds its way into every college biology textbook and usually is mentioned in the chemical kinetics chapter of general chemistry textbooks. Because so many biochemical reactions [2] are mediated by enzymes, it is important to understand their kinetics. Biology students [3] may encounter enzyme kinetics before seeing chemical kinetics in the second semester of general chemistry. Enzyme kinetics is a natural extension of chemical kinetics concepts, although, it can appear to use a completely different language. Since enzyme kinetics is an important biological topic in molecular biology and microbiology, can general chemistry instructors get it into the curriculum? This chapter introduces an interactive Microsoft Excel spreadsheet (or Excelet) and accompanying guided-inquiry activity to expose students to the kinetics of enzyme reactions, including analyzing data, dealing with experimental error, and observing the effects of inhibitors. Data analysis by both linear and non-linear regression analyses is covered as well as analysis of experimental results. The use of Excelets as discovery learning tools has been recently described in [4, 5]. To use this Excelet, students need Microsoft Excel with the Analysis ToolPak and Solver Add-in loaded (instructions are included in the Excelet on the needed Add-ins tab). Students will navigate using the tabs at the bottom of the screen (see Fig. (6.1)). Students should have an introduction to using the interactive features of Excelets and how to explore a variable beforehand. Data analysis is Mark Lau and Stephen Sugden (Eds) All rights reserved – c○2011 Bentham Science Publishers Ltd.
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